Digital instruments for measurement and display of waveforms of time-varying signals are well known in the prior art. Such instruments present the signal information as a set of coordinate points, for example on a cathode-ray tube screen (CRT). Such digital instruments generally operate by sampling each signal a multiplicity of times, measuring and recording the samples, and simultaneously or later displaying the sampled voltage values as coordinate points, each of which has an ordinate value proportional to the measured voltage, and an abscissa value equal to the sample number corresponding to that voltage. Because the samples are taken at regular time intervals relative to the sweep trigger(s), or "start of the waveform", the sample numbers, and abscissa values, are linearly related to the times at which the samples were taken.
One of the disadvantages of such prior art instruments is that if the signals being sampled and viewed are periodic, problems can arise due to an effect known as aliasing. Aliasing occurs if the signal frequency is greater than half the frequency of sampling (which is called the Nyquist frequency, f.sub.N), in which case the displayed pattern of coordinate points can be exceedingly misleading to the viewer. Though each point may be shown at exactly the correct voltage and time position, the overall effect can be deceptive. For example, in case of a sine wave signal having a frequency slightly greater than 2f.sub.N, it is possible to get a display of sampling points indicating the presence of a sinusoid, but which appears to the operator to be at a much lower frequency. The same situation could occur with a different waveform, such as a triangular wave, in which case the aliasing pattern could also be a triangular wave at a lower frequency, all of which adds to the deceptive effect of aliasing due to signals greater than the Nyquist frequency.
Therefore, even though all high frequencies do not produce believable patterns to the viewing operator, such a large number of frequencies do cause this aliasing effect that unless the operator has some form of dependable advance knowledge that the signal frequency is below the critical frequency, he will either believe the deceptive aliased pattern, or at best be concerned that he is being mislead.
Various measures can be taken to confirm that the signal waveform is not an alias. One such measure is to reject, by filtering, all frequencies above f.sub.N. This solution is impractical in digital oscilloscopes which usually provide for many different sampling rates, and therefore would require that the filter must have many selectable cut-off frequencies ranging, for example, from a small fraction of one hertz to many megahertz. Filtering, even if practical, would have the disadvantage of not allowing the operator to be aware of the existence of higher frequency signals. Another measure for testing for aliasing is to use a very high sampling rate, using one filter to reject signals having frequencies beyond the corresponding critical frequency. However, such tests are a considerable nuisance to the operator, and do not work in the situation in which a signal only occurs once. Also, in the common situation in which the signal is an amplitude modulated carrier, neither testing nor filtering is possible. Sampling frequencies must necessarily be low enough to view the modulation pattern, which may, for example, be a one kilohertz sine wave. In that case, if the oscilloscope has the ability to display only one thousand points, the sampling frequency cannot be greater than one megahertz, or less than one cycle of the modulation will be seen. Yet, the carrier may have a frequency of several megahertz, and will be subject to aliasing. In that situation, the coordinate display often is completely useless and may often show no modulation envelope at all.